涉及导数的一类全纯函数的正规族

Normal Families of A Kind of Holomorphic Functions Concerning Derivatives

主要使用Zalcman引理来研究全纯函数的正规族,得到了如下的结论:令F为|z|<1内的一族全纯函数,n是一个正整数,a,b是两个复数且满足a≠0,∞,b≠∞.若F满足:Ⅰ)■f∈F,如f有零点,则f的零点重级大于等于3;和Ⅱ)当n≥4时,对F的每一对函数G和H,G″-aG^(n,)与H″-aH^n分担b.则F在|z|<1内正规.

In this paper,we mainly use Zalcman lemna to investigate normal families of holomorphic functions,and gets the following results：let F be a family of holomorphic functions in ｜z｜1,n is a positive integer,a,b are two complex numbers and satisfies a≠0,∞,b≠∞,If F satisfies：（Ⅰ） for■f∈F,if f has zeros,then the multiplicity of zeros of f is greater than or equal to 3;and（Ⅱ）when n≥4,for every pair of functions G and H belong to F,G＂ - aG^n and H＂ - aH^n share b.then F is normal in ｜z｜1.